## Chauvenet's Treatise on Elementary Geometry |

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ABCD adjacent altitude angles are equal base BOOK called centre chord circle circumference circumscribed coincide common cone consequently construct contained Corollary cylinder Definition describe diagonal diameter diedral angle difference distance divided draw drawn equal equally distant equivalent Exercise extremities faces fall figure follows formed four frustum given line given point given straight line greater half Hence included angle increased indefinitely inscribed intersection isosceles joining lateral edges length less limit locus mean measure meet middle point one-half opposite parallel parallelogram parallelopiped pass perimeter perpendicular placed plane polyedron polygon prism problem proportional Proposition VII prove pyramid radii radius ratio rectangle rectangular regular polygon respectively right angles Scholium segment sides similar sphere spherical square Suggestion surface tangent Theorem third tion triangle triangle ABC triangular unit vertex vertices volume

### Popular passages

Page 137 - Two triangles having an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles.

Page 38 - The sum of the three angles of any triangle is equal to two right angles.

Page 133 - The area of a rectangle is equal to the product of its base and altitude.

Page 249 - A truncated triangular prism, is equivalent to the sum of three pyramids whose common base is the base of the prism, and whose vertices are the three vertices of the inclined section.

Page 117 - The square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides.

Page 29 - The perpendicular is the shortest line that can be drawn from a point to a straight line.

Page 282 - The area of a lune is to the surface of the sphere as the angle of the lune is to four right angles, or as the arc which measures that angle is to the circumference.

Page 52 - The straight line joining the middle points of two sides of a triangle is parallel to the third side, and equal to half of it.

Page 268 - Any line or plane tangent to a sphere is perpendicular to the radius drawn to the point of contact.

Page 234 - Two rectangular parallelopipeds having equal altitudes are to each other as their bases. Let a, b and c...